OK, next time, could you please state these things completely?? The wikipedia article says that [itex]Aut(H\times K)\cong Aut(H)\times Aut(K)[/itex] if the groups are finite, abelian and of coprime order!! You need those conditions.

As for the proof, try to prove it in these steps

Given an automorphism [itex]f\times K\rightarrow H\times K[/itex], then f(H)=H and f(K)=K.